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Donald Trump told Ted Cruz that if he wants to knock New York "you've got to go through me"

Cruz hit back against Trump this week after more than a week of deflecting his attacks on his birth in Canada

Washington (CNN)New York Rep. Peter King had some sharp words for Republican presidential candidate Ted Cruz on Thursday, in the wake of the Texas senator's attempt to criticize Donald Trump.

Cruz, who had been playing nice with Trump for much of the campaign, recently attempted to disparage the real estate mogul by accusing him of possessing "New York values." The attack came after Trump raised questions over the Canadian-born Cruz's ability to serve as president.

Trump "may shift in his new rallies to playing 'New York New York,' because you know Donald comes from New York and he embodies New York values," Cruz said Tuesday on "The Howie Carr Show" on Boston-based WRKO.

"Memo to Ted Cruz: New York Values are the heroes of 9/11; the cops who fight terror; and the people you ask for campaign donations. Go back under a rock," King said in a statement to CNN Thursday.

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Trump has also cited 9/11 as an example of why "New York values" are something to be proud of, rather than a turn-off for voters.

"New York is an amazing place with amazing people," Trump said on Bloomberg's "With All Due Respect." "We took a big hit with the World Trade Center -- worst thing ever, worst attack ever in the United States, worse than Pearl Harbor because they attacked civilians, they attacked people having breakfast and frankly if you would've been there and if you would've lived through that like I did with New York people -- the way they handled that attack was one of the most incredible things that anybody has ever seen."

Trump has been harping on Cruz's Canadian birth for almost two weeks -- with some success reflected in Iowa polls -- but Cruz opened up his own line of attack Tuesday, portraying Trump as a typical New Yorker more aligned with Democrats and liberals then Republican who will head to the polls shortly.

Cruz unseated Trump last month atop the Iowa polls and has maintained his position there with just three weeks left until Republicans head to the caucuses. But the latest Des Moines Register/Bloomberg poll showed a large dip in Cruz's support -- an apparent vindication of Trump's decision to attack him relentlessly with the "birther" question.

King has long been critical of Cruz, including the Texas senator's fall 2013 efforts to defund the Affordable Care Act, which led to a federal government shutdown of more than two weeks.

"Shutting down the federal government and reading Dr. Seuss on the Senate floor are the marks of a carnival barker not the leader of the free world," King said in a March 2015 written statement.